The present invention relates to a positional control system and to apparatus for providing control signals giving the positional control system an improved response characteristic.
Conventional positional control systems are comprised of a servo arrangement for driving a load to selected positions, control circuitry for operating the driving arrangement to move the load, and signalling circuitry for generating error signals to which the control circuitry is responsive to actuate the driving arrangement. A theoretically perfect positional control system would (1) drive the load along the shortest path to a selected position, (2) drive the load to the selected position in the shortest possible time, and (3) stop the load at the selected position with no oscillatory motion. Stated another way, the ideal response to such control systems is one in which the positional error is reduced exactly to zero with no overshoot and in the minimum time compatible with the capabilities of the available components of the system.
Conventional second order positional control systems have been implemented in an attempt to realize a theoretically perfect control system. In such second order systems, positional error signals are generated using a position transducer and are indicative of a difference between the position of the load and the selected position. A function generator is responsive to these error signals and generates signals representing the optimal velocity that the load should have at various positions as it moves towards the selected position. A rate signal generator or transducer is also employed to generate signals corresponding to the velocity of the load at the various positions, and these velocity signals are subtracted from the optimal velocity signals to generate velocity error signals which drive the driving arrangement. The driving arrangement then increases or decreases the speed of the load to meet the three requirements mentioned above. One type of such positional control system is known as a "bang-bang" controller in which the driving arrangement is operated at maximum acceleration until the midpoint between the initial and selected positions is reached and at maximum deceleration from the midpoint to the selected position.
There are positional control systems moving a load to a selected position which are known as third order systems. That is, these systems include relay servos having driving motor-load units with a third-order differential equation. These systems employ the same concept of optimum performance as the second order systems, i.e., they attempt to move a load over the shortest distance in the minimum amount of time to position the load at the selected position without any oscillatory motion. The relay servo should operate so that at the selected position, the positional error, the velocity error and the acceleration error are zero. Such third order systems have a driving arrangement which is responsive in part to acceleration signals representing the acceleration of the load at each position on its movement towards the selected position. The acceleration signals used by the third order positional control systems are obtainable from positional error and velocity signals mentioned above in connection with second order systems.
In order for such second order or third order systems to operate optimally, in fact for any system of a higher or lower order, it is desirable that the signals which drive the driving arrangements of each system be derived from positional error and velocity signals which are free from nonlinearities and discontinuities. It is also desirable to generate such positional error and velocity signals which are free of nonlinearities and discontinuities from a single transducer; however, until now this has been a problem.